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In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set.

The inverse nodal problem for the Sturm–Liouville operator is the problem of finding the potential function q and the boundary conditions using the nodal points. The purpose of this paper is to present a method for solving the inverse nodal problem for a singular differential operator on a finite interval. We find asymptotic formulas for nodal points and… (More)

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

- Etibar S Panakhov, Murat Sat
- 2013

In this paper, we considered an inverse problem with two given spectrum for a boundary value problem with aftereffect and eigenvalue in the boundary condition and we showed that transformation operator was generalized degeneracy and we obtained a new proof of the Hochstadt's theorem concerning the structure of the difference q(x) q(x).

It is well known that the two spectra {λ n } and {µ n } uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type () 2 1 2 r r + + (where is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the… (More)

In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt's theorem concerning the structure of the difference q(x) − ˜ q(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin 2 x at the points… (More)

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